Question

I need help with the final part of this problem - ​(c) Interpret the coefficient of determination and comment on the adequacy of the linear model - all 4 parts. Thank you so much for all the help!

The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r = −0.963. The​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is ŷ -0.0070 x +44.4623.

Car   Weight (pounds), x   Miles per Gallon, y
1   3,765   18
2   3,984   17
3   3,530   21
4   3,175   23
5   2,580   26
6   3,730   18
7   2,605   25
8   3,772   17
9   3,310   20
10   2,991   25
11   2,752   26

(a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per​ gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is 92.7​%.

​(b) Construct a residual plot to verify the requirements of the​ least-squares regression model. Choose the correct graph below.

• C.

250032504000-202Weight (pounds)Residual

• A coordinate system has a horizontal axis labeled Weight in pounds from 2500 to 4000 in increments of 750 and a vertical axis labeled Residual from negative 2 to 2 in increments of 0.5. The following points are plotted: (2600, negative 0.4); (2600, negative 1.25); (2750, 0.8); (3000, 1.45); (3200, 0.75); (3300, negative 1.3); (3550, 1.2); (3750, negative 0.4); (3750, negative 0.15); (3750, negative 1.1); (4000, 0.4). A dashed horizontal line crosses the vertical axis at 0. The points appear scattered above and below the line and do not appear to follow a pattern. All coordinates are approximate.
• Your answer is correct.

​(c) Interpret the coefficient of determination and comment on the adequacy of the linear model.

__?__% of the variance in GAS MILEAGE or WEIGHT is EXPLAINED or NOT by the linear model. The​ least-squares regression model appears to be INAPPROPRIATE or APPROPRIATE, based on the residual plot.

​(Round to one decimal place as​ needed.)

Answer 1

c)

92.7% of the variance in GAS MILEAGE is EXPLAINED by the linear model.

The​ least-squares regression model appears to be APPROPRIATE, based on the residual plot.